Statistica Sinica 17(2007), 1533-1548

LEAST ABSOLUTE DEVIATIONS ESTIMATION FOR THE

ACCELERATED FAILURE TIME MODEL

Jian Huang$^{1}$, Shuangge Ma$^2$ and Huiliang Xie$^1$

$^1$University of Iowa and $^2$Yale University

Abstract: The accelerated failure time (AFT) model assumes a linear relationship between event time and covariates. We propose a robust weighted least-absolute-deviations (LAD) method for estimation in the AFT model with right-censored data. This method uses the Kaplan-Meier weights in the LAD objective function to account for censoring. We show that the proposed estimator is root-$n$ consistent and asymptotically normal under appropriate assumptions. It can also be easily computed using existing software, which makes it especially useful for data with medium to high dimensional covariates. The proposed method is evaluated using simulations and demonstrated on two clinical data sets.

Key words and phrases: Asymptotic normality, Kaplan-Meier weights, least absolute deviations, right censored data, robust regression.